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Fungrim entry: 4c7aeb

Un ⁣(cos ⁣(x))sin ⁣(x)=sin ⁣(nx)U_{n}\!\left(\cos\!\left(x\right)\right) \sin\!\left(x\right) = \sin\!\left(n x\right)
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
U_{n}\!\left(\cos\!\left(x\right)\right) \sin\!\left(x\right) = \sin\!\left(n x\right)

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
Fungrim symbol Notation Short description
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Mul(ChebyshevU(n, Cos(x)), Sin(x)), Sin(Mul(n, x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC